This paper investigates sandwich beams' forced vibrations reinforced with graphene platelets (GPLs) based on higher-order shear deformation theory. A novel nonlinear reinforcement distribution based on the power-law method is proposed to model functionally graded (FG) graphene platelet reinforced composite face sheets. Due to the manufacturing constraints, the face sheets are considered laminated so that the weight fraction of GPLs in each layer is constant and varies functionally along with the thickness of the beam. Also, the effective material properties of each layer have been calculated using the Halpin Tsai micro-mechanical model. The nonlinear partial equations of motion are derived using Hamilton's principle in the third-order laminated beam model framework. Afterward, the governing equations of motion are discretized to a system of ordinary nonlinear equations by applying Galerkin's method and solved using an analytical approach. Numerical results obtained from the presented work are compared and validated with the literature. The results show that the proposed model can predict the desired GPLs distribution pattern in the face sheets according to the sandwich layers thickness ratio, the amount of the external force, and the total weight fraction of the GPLs. Also, it is found that increasing the concentration of GPLs in the outer layers can significantly increase the vibration frequency of the system and reduce its nonlinearity. However, the core-to-beam thickness ratio is highly effective in how the reinforcement pattern affects the system behavior. Besides, the external excitation characteristics have notable effects on the system's behavior, and multivaluedness in response will be observed depending on the frequency of excitation.

本文基于高阶剪切变形理论研究了用石墨烯片 (GPL) 增强的夹层梁的受迫振动。提出了一种基于幂律方法的新型非线性增强分布来模拟功能梯度 (FG) 石墨烯薄片增强复合面板。由于制造限制，面板被认为是层压的，因此每层中 GPL 的重量分数是恒定的，并且随着梁的厚度在功能上发生变化。此外，每层的有效材料特性已使用 Halpin Tsai 微机械模型进行计算。在三阶层合梁模型框架中使用哈密顿原理推导出非线性运动偏方程。之后，通过应用伽辽金方法将运动控制方程离散为一个普通非线性方程组，并使用解析方法求解。从目前的工作中获得的数值结果与文献进行了比较和验证。结果表明，所提出的模型可以根据夹层厚度比、外力大小和 GPL 的总重量分数来预测面板中所需的 GPL 分布模式。此外，还发现增加外层GPLs的浓度可以显着增加系统的振动频率并降低其非线性。然而，核心与梁的厚度比在钢筋模式如何影响系统行为方面非常有效。除了，